Following a collegiate career at the University of Wisconsin–Madison, Mueller was the sixth overall pick of the 2018 MLS SuperDraft, joining Orlando City where he became the club's all-time leading appearance maker during a four-season spell.
Mueller joined Scottish club Hibernian in January 2022, but left them after four months and returned to MLS with Chicago Fire.
Mueller grew up in Schaumburg, Illinois and played college soccer at the University of Wisconsin from 2014 to 2017, scoring 22 goals in 75 regular season matches.
In July 2019, Mueller was part of the Orlando City team alongside Nani and Sebas Méndez that won the 2019 MLS All-Star Skills Challenge, beating teams from the MLS All-Stars and Atlético Madrid to win the $25,000 prize for charity with Mueller notably the only player to successfully complete a scissors kick during the volleys round.
On July 22, 2021, Scottish Premiership side Hibernian announced they had signed Mueller on a free transfer agreement, which would see him join the club on January 1, 2022.
[19] Hibs chief executive Ben Kensell said that Mueller had struggled to "adapt to the pace and physicality" of Scottish soccer.